Statistics and Their Levels

First part of the article: Statistics in Poker (1) – Basics (1)

The Pyramid system – is a scheme that illustrates which statistics depend on others and why.

To make it easier to understand statistics and their interdependence, we will use a pyramid scheme. Imagine that:

The higher the level of the statistic, the rarer the situation defined by the statistic occurs. Statistics at the top indicate a specific opponent's action that is performed infrequently.
The higher the level of the statistic, the more hands need to be played against the opponent to interpret that statistic correctly.
Higher-level statistics rely on lower-level statistics (directly or indirectly).

The basis of this level scheme is that some actions defined by certain statistics can only occur when a certain other action has been performed.

For example: a flop c-bet can only occur when the opponent has raised pre-flop and is the pre-flop aggressor. That's why C-bet statistics are based on pre-flop raise statistics.

In the pyramid system below, statistics are divided into different levels, which are marked with Roman numerals. For example: I VPIP or II 3b.

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Most Commonly Used Statistics

Not all statistics can be classified into a single, specific level of this pyramid – we have divided these statistics, which can describe an opponent's playing style, into several different levels.

AF (aggression factor)

The AF statistic indicates the ratio of aggressive actions (bet/raise) to passive actions (call). The formula for this statistic is quite simple: (Bets + Raises) / Calls. If a player's aggression factor value is 1.0, it means that this player bets and raises as often as they call.

If the aggression factor is less than 1, they perform passive actions more often than aggressive ones. However, if the aggression factor is greater than 1, it is the opposite – they perform aggressive actions more often.

WTS (went to showdown)

The WTS statistic indicates the percentage of hands played with which the player went to showdown from the flop. This statistic does not indicate aggression, so whether the opponent bet, called, or checked – it doesn't matter. Therefore, to interpret this statistic correctly, you need to pay attention to the actions the opponent took and their aggression factor.

Sample size

This is probably the most important, but at the same time, the least informative statistic about the player. It indicates how many hands the player has received at the table. Whether the opponent played the hand or just folded it pre-flop – it doesn't matter.

If a 15/10 opponent played 100 hands, it means they were dealt 100 hands, of which they put money into the pot with 15 hands. They raised with 10 hands and called a raise or limped from the SB position with 5 hands. This example perfectly shows how little 100 played hands tell us about, for example, the opponent's hand range with which they just call.

Based on statistics, the sample size is especially important because it helps determine approximately how accurate other statistics are. The higher the level of the statistic, the more important the sample size is. In poker, everything, including the distribution of dealt cards, depends on variation, so the larger the sample size, the more accurate other statistics are.

First Level – I

The first level describes statistics that do not depend on any other statistics. For these statistics to be at least somewhat accurate, the opponent's sample size can be small, for example, less than 100.

I VPIP (Voluntary put $ in Pot)

The VPIP statistic is one of the main statistics. It indicates the percentage of hands the opponent invests in the pot. This statistic includes limping, calling, and raising. Remember that auto-post blinds are not counted.

Many statistics depend on this statistic. Moreover, based on this statistic, you can predict the opponent's post-flop hand range.

VPIP also affects the PFR statistic because, as mentioned, raising is also included in this statistic. After all, when a player performs this action, they voluntarily put money into the pot, right?

I PFR (Preflop Raise)

PFR indicates the percentage of hands played with which the player raised pre-flop. This statistic includes open-raising (the first raise pre-flop) as well as other raises (3-bet, 4-bet, etc.). This statistic is a good indicator of aggression.

I calling range

Well, the calling range is not exactly a statistic, but it is very easy to understand. This hand range indicates the percentage of hands the opponent calls pre-flop. The formula to calculate it is very simple – just subtract PFR from VPIP, and you have the answer.

I ATS (Attempt to Steal)

The Attempt-to-steal statistic is the first specific pre-flop statistic. It indicates the percentage of hands the player open-raises from late positions (CO, BU, SB). For many good players, the ATS statistic is higher than the PFR statistic.

This is because the later the position the player is in and the fewer players are left after them, the more often players tend to open-raise.

I Fold to Steal

The Fold-to-steal statistic indicates how often the player does not defend their blinds when they are being stolen, i.e., they just fold their cards. This statistic includes only those situations when the player is in the blinds position and when there is an open-raise from a late position. Their reaction from the blinds position to, for example, a UTG open-raise does not affect the fold-to-steal statistic.

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Second Level – II

Second-level statistics depend on first-level statistics. Therefore, when trying to interpret the statistics at this level, you should always pay attention to the statistics at the first level.

Since the actions represented by the statistics at the second level occur much less frequently in the game, a much larger sample size is required for these statistics. For these statistics to be at least somewhat accurate, the opponent must have played more than 500 hands.

II 3-bet

3-bet is the first second-level statistic. It depends on the previous first-level action: open-raise.

A 3-bet action cannot be performed if no one has raised before the opponent. Therefore, the 3-bet statistic indicates the percentage of hands the player 3-bets. Since this action occurs much less frequently, a much larger sample size is needed to interpret it correctly.

So, as you may have noticed, first-level statistics require only one person, but second-level statistics require other players to perform certain actions.

Correlation: Player (A) raises – Player (B) 3-bets

II (f3b / c3b) Fold to 3-Bet / Call 3-Bet

Fold to 3-bet / Call 3-bet statistics strongly depend on the dynamics of the limits. The more aggression there is pre-flop, the more often the player will face a 3-bet and the more often they will have to make a decision. In passive limits, you usually need a larger sample size than in aggressive limits.

So, as you have noticed, this statistic requires the following sequence of actions: open-raise, someone 3-bets, the opponent folds or calls the 3-bet.

Correlation: Player (A) raises pre-flop “PFR” – Player (B) 3-bets – Player (A) folds/calls

II Cbet (continuation bet)

Cbet statistics indicate how often a player makes a continuation bet on the flop, being the pre-flop aggressor. This statistic depends on the flop range and I PFR, a first-level statistic.

Correlation: Player (A) raises pre-flop “PFR” – Player (B) calls – Player (A) Cbets

II Fold to Continuation Bet

Fold-to-continuation bet statistics indicate the player's reaction to a continuation bet, i.e., how the player reacts in situations where they called pre-flop and face a continuation bet on the flop made by the pre-flop aggressor.

Correlation: Player (A) raises pre-flop “PFR” – Player (B) calls – Player (A) Cbets – Player (B) folds.

Donk bet (only when out of position against the pre-flop aggressor)

A donk bet is a bet made by the opponent on the flop against the pre-flop aggressor. This statistic indicates how often a player makes this type of bet on the flop. It also applies to re-raised pots.

Correlation: Player (A) raises – Player (B) calls – Player (B) makes the first bet against the aggressor II Donk bet on the flop

Third Level – III

The actions described by third-level statistics are seen even less frequently because these statistics depend on second-level statistics. You will encounter these statistics in only a few hands. To rely on third-level statistics, the sample size should be greater than 1,000. Almost none of the third-level statistics have a sample size limit. You must interpret these statistics very accurately, which means you must also pay attention to lower-level statistics and the game situation itself.

III Raise Continuation Bet

This statistic indicates how often a player raises the pre-flop aggressor's continuation bet on the flop. This includes check/raises and raises in position. This statistic also applies to re-raised pots. If you are playing against a very aggressive opponent, you can apply the raise-cbet statistic after playing a few hundred hands against the opponent.

Correlation: Player (A) raises – Player (B) calls – pre-flop aggressor (A) Cbets – Player (B) raises

In this case, we see that all three levels of statistics are used in the sequence:

Player (A) raises – Player (B) calls – I level statistics.

pre-flop aggressor (A) Cbets – II level statistic.

Player (B) raises – III level statistic.

III 4-bet

The 4-bet statistic indicates how often a player raises another player's 3-bet (II level statistic). A 4-bet usually indicates a strong move. You can usually assume that: the lower the limit and the more passive the opponent, the stronger the hand they have when 4-betting.

To 4-bet, a 3-bet must have been made before, so a 4-bet is a rarely seen action at the tables. The more passively players play pre-flop in certain limits, the less often a player gets the opportunity to 4-bet. Therefore, this statistic depends on the dynamics of the limits.

Correlation: Player (A) raises – Player (B) 3-bets – Player (A or C) 4-bets

III Float / Raise Turn Cbet

Float is usually an action where we take the initiative from the pre-flop aggressor. This statistic simply indicates how often this action is performed. You can draw conclusions about the strength of the hand only if you rely on other statistics as well. The float action is most often performed on the turn.

Correlation: Player (A) makes a raise pre-flop – Player (B) calls – pre-flop aggressor Player (A) Cbets the flop – Player (B) calls – after the pre-flop aggressor Player (A) checks/bets on the turn, Player (B) bets/raises

III Second barrel / Turn Cbet

Second barrel is a continuation bet on the turn, which is made after a continuation bet on the flop.

Correlation: Player (A) makes a raise pre-flop – Player (B) calls – Player (A) Cbets the flop – Player (B) calls – Player (A) Cbets the turn

Fourth Level – IV

The actions indicated by the statistics belonging to the fourth level occur very rarely because they consist of a fairly long chain of actions that depend on lower levels. To rely on these statistics, the sample size should be much larger than 1,000 hands.

IV Third barrel / River Cbet

Third barrel is a continuation bet on the river, which is made after a continuation bet on the turn. A third barrel bet can only be made when the pre-flop aggressor has made bets on both the flop and the turn.

Correlation: Player (A) makes a raise pre-flop – Player (B) calls – Player (A) Cbets the flop – Player (B) calls – Player (A) Cbets the turn – Player (B) calls – Player (A) Cbets the river

IV Fold to 4-bet / Call 4-bet / Ship

These statistics indicate how often a player performs a certain action when facing a III 4-bet. Depending on the stack size, the player can call or ship (push all-in) or the third option is to fold.

Correlation: Player (A) raises – Player (B) 3-bets – Player (A or C) 4-bets – Player (B) f4b / c4b / ships

IV 5-bet / Ship / Fold

Depending on the stack size, when facing a 4-bet, the player can push all their chips, 5-bet, or fold their cards.

Correlation: Player (A) raises – Player (B) 3-bets – Player (A or C) 4-bets – Player (B) 5-bets / ships / folds

Summary

So, in the first part of this article, you learned what statistics are and what they tell about your opponent's game. Moreover, we reviewed the main statistics and learned which level of the pyramid each statistic belongs to.

In the next part, you will deepen your knowledge of statistics, learn to interpret them, and fully understand the concept of “sample size”.